Thompson was the top scorer for Linfield last season, helping them finish eight points clear at the top of the Irish Premier League.
Stockport had been linked with the forward Gary Hooper, who opted to join Scunthorpe from Southend earlier this week.
Despite having the opportunity to take part in the Champions League, Jeffery has said that he fully understands why the 24-year-old would want to move to Edgeley Park.
"It would not be morally right to even think about standing in Peter's way," he said.
"He made a career decision and wants to play at the highest level he possibly can.
"We are still talking to Stockport but things have moved on quickly and I am not sure he will get the chance to play one last game for us on Wednesday (against Dinamo Zagreb)."
County have reportedly offered around £100,000 plus incentives to Linfield for the striker, who scored 44 goals last season.